"There's an increasing sense that Thompson is not conservative enough -- only 34 percent of voters say they want him to be the nominee, while 50 percent say they would prefer someone 'more conservative,'" noted PPP in its release.

Thompson's opponents have been focusing on his past support for health care reform. For example, Thompson -- who also served as President George W. Bush's Secretary of Health and Human Services -- once backed the individual mandate, and in 2009 he praised a leading Democratic version of reform legislation. He now says he wants to repeal Obamacare.

Hovde, meanwhile, is emerging as the conservative alternative to Thompson, according to PPP, even though Neumann has the backing of the Club for Growth and of Tea Party favorites like Sens. Mike Lee (R-Utah) and Rand Paul (R-Ky).

While non-Tea Party Republicans in the PPP poll split evenly between Hovde and Thompson, Hovde has an 18-point advantage among those who identify with the Tea Party.

"There's reason to think Hovde's lead could get wider between now and the primary -- he still has only 59 percent name recognition, compared to 84 percent for Thompson. Among the voters who are familiar with Hovde he leads Thompson 47-21, suggesting that as he becomes better known in the final weeks of the campaign his fortunes could continue to improve," added PPP.

Hovde recently gained national attention for saying he was tired of the media covering sad stories about poor people who can't get their food stamps.

Hovde said he would love to see the press stop covering sad stories about low-income individuals who can't get benefits and start covering issues like the deficit more frequently.

"I just pray that you start writing about these issues," said Hovde at a speech in June, referring to the debt and government spending. "I just pray. Stop always writing about, 'Oh, the person couldn't get, you know, their food stamps or this or that.' You know, I saw something the other day -- it's like, another sob story, and I'm like, 'But what about what's happening to the country and the country as a whole?' That's going to devastate everybody."

The winner of the primary will face Rep. Tammy Baldwin (D-Wis.) in November. In the PPP poll, Hovde leads Baldwin 45 percent to 44 percent, while Thompson and Baldwin are tied at 45 percent.

HuffPost Pollster's analysis of the polling in the Wisconsin Senate GOP primary:

Also on HuffPost:

Below-The-Belt Political Attacks

Below-The-Belt Political Attacks

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Lee Atwater: Smear Pioneer

Negative campaigning has become more effective since 1828, though at times no less brutal. Many attribute this growing efficiency to the legacy of Republican strategist Lee Atwater. The former RNC chairman may have been best known as a driving force behind political ads such as the iconic Willie Horton commercial against Michael Dukakis in 1988, but his past involvement in smear campaigns is much deeper. Slate reports on Atwater's earlier career:
In 1973, the 22-year-old protégé of South Carolina Sen. Strom Thurmond began his consulting career by publicizing the fact that Tom Turnipseed, a candidate for the state Senate, had undergone shock therapy as a young man: "They hooked him up to jumper cables" became the catchphrase that sunk Turnipseed's candidacy. Five years later, Atwater helped to defeat Max Heller, a Holocaust survivor running for U.S. Congress, by secretly enlisting a third candidate to enter the race and stir up anti-Semitic sentiment. Atwater finagled his way into a minor post in the Reagan administration, but it was as the director of George H.W. Bush's 1988 presidential campaign (and mastermind of the Willie Horton TV ads) that he found his true Machiavellian voice.